1 a) What is the probability of you drawing three face cards from a well shuffled deck if you keep each card you draw?
Since there are 12/52 face cards would it be first 12/52, then 11/51 then 10/50? I am confused about this
b) What is the probability of you drawing three face cards from a well shuffled deck if you replace each card you draw?
a) To find the probability of drawing three face cards from a well-shuffled deck when you keep each card you draw, you can calculate the probability of each individual event and multiply them together.
The first card you draw has a 12/52 probability of being a face card since there are 12 face cards out of 52 total cards in the deck.
After drawing the first face card, there are now 51 cards remaining in the deck, with 11 face cards left. So the probability of drawing another face card on the second draw is 11/51.
Similarly, after the second face card is drawn, there are now 50 cards remaining, with 10 face cards left. So the probability of drawing a third face card on the final draw is 10/50.
To find the overall probability, multiply the individual probabilities together:
(12/52) * (11/51) * (10/50) = 0.0176 or 1.76%
b) If you replace each card you draw, the probability of drawing a face card on each draw remains the same for each card drawn because each card is being replaced in the deck.
So the probability of drawing a face card on the first, second, and third draw is still 12/52 for each draw.
To find the overall probability, simply raise the probability of drawing a face card on each draw to the power of the number of draws:
(12/52) * (12/52) * (12/52) = (12/52)^3 = 0.049 or 4.9%
a) To calculate the probability of drawing three face cards from a well-shuffled deck without replacement, you need to multiply the probabilities of drawing each face card.
First, you correctly identified that there are 12 face cards in a standard deck of 52 cards. So for the first draw, the probability of drawing a face card is 12/52.
On the second draw, since you did not replace the card you drew, there are now only 51 cards left in the deck, and the number of face cards decreases to 11. So the probability of drawing a face card on the second draw is 11/51.
On the third draw, there are 50 cards left in the deck and only 10 face cards remaining. Therefore, the probability of drawing a face card on the third draw is 10/50.
To find the overall probability of drawing three face cards, you multiply the probabilities for each draw:
(12/52) * (11/51) * (10/50) = 0.064
So the probability of drawing three face cards without replacement is approximately 0.064, or 6.4%.
b) If you replace each card you draw, then the probability of drawing a face card on each subsequent draw remains the same.
Since there are initially 12 face cards in the deck and 52 total cards, the probability of drawing a face card on each draw is 12/52.
To calculate the overall probability of drawing three face cards with replacement, you multiply the probabilities for each draw:
(12/52) * (12/52) * (12/52) = 0.059
So the probability of drawing three face cards with replacement is approximately 0.059, or 5.9%.